Recent development of next generation sequencing (NGS) technologies has led to the identification of structural variants (SVs) of genomic DNA existing in the human population. Several SV detection methods utilizing NGS data have been proposed. However, there are several difficulties in analysis of NGS data, particularly with regard to handling reads from duplicated loci or low-complexity sequences of the human genome. In this paper, we propose SVEM, a novel statistical method to detect SVs with a single nucleotide resolution that can utilize multi-mapped reads on breakpoints. SVEM estimates the amount of reads on breakpoints as parameters and mapping states as latent variables using the expectation maximization algorithm. This framework enables us to handle ambiguous mapping of reads without discarding information for SV detection. SVEM is applied to simulation data and real data, and it achieves better performance than existing methods in terms of precision and recall.